Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens

Impact-loaded, precracked Charpy specimens often play a crucial role in irradiation surveillance programs for nuclear power plants. However, the small specimen size B = W = 10 mm limits the maximum value of cleavage fracture toughness J_c that can be measured under elastic—plastic conditions without loss of crack tip constraint. In this investigation, plane strain impact analyses provide detailed resolution of crack tip fields for impact-loaded specimens. Crack tip stress fields are characterized in terms of J—Q trajectories and the toughness-scaling model which is applicable for a cleavage fracture mechanism. Results of the analyses suggest deformation limits at fracture in the form of b > MJ_c/σ₀, where M approaches 25–30 for a strongly rate-sensitive material at impact velocities of 3–6 m s⁻¹. Based on direct comparison of the static and dynamic J values computed using a domain integral formulation, a new proposal emerges for the transition time, the time after impact at which interial effects diminish sufficiently for simple evaluation of J using the plastic η factor approach.     

Study on the effect of the crack length on the JIC value

The ductile fracture tests are carried out using compact type (CT) specimen, three point bend specimen and center cracked tension (CCT) specimens made of A533B steel and aluminum alloy with different crack lengths. The effect of the crack tip constraint on the microscopic fracture behavior is studied by the scanning electron microscope (SEM). It is shown that the apparent J_IC value increases due to the decrease of the crack tip constraint. It is pointed out that the increase of the apparent J_IC value is partly due to the error of the conventional equation to estimate the J value. Based on the FEM analyses, these apparent J_IC values are corrected and are compared with the valid J_IC values. The good co-relation between apparent J_IC value and the Q factor, proposed by O'Dowd and Shih, is shown for all the specimens. The FEM analyses based on the Gurson's constitutive equation is also carried out. The effect of the constraint on the crack tip field is discussed.     

On the dynamic fracture toughness and crack tip strain behavior of nuclear pressure vessel steel: Application of electromagnetic force

This paper is concerned with the application of the electromagnetic force to the determination of the dynamic fracture toughness of materials. Taken is an edge-cracked specimen which carries a transient electric current I and is simply supported in a steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen, which is then deformed to fracture in the opening mode of cracking.Using the electric potential and the J - R curve methods to determine the dynamic crack initiation point in the experiment, together with the finite element method to calculate the extended J-integral with the effects of the electromagnetic force and inertia, the dynamic fracture toughness values of nuclear pressure vessel steel A508 class 3 are evaluated over a wide temperature range from lower to upper shelves.The strain distribution near the crack tip in the dynamic process of fracture is also obtained by applying a computer picture processing.     

Characteristics relevant to ductile failure of bimetallic welds and evaluation of transferability of fracture properties

Life management and structural integrity assessment of bimetallic welds in its state-of-the-art form relies on practical methods derived on the basis of years of experience in operation and simplistic strength of materials analyses. The complex conditions and properties of the weldment, as resulting from the elaborate interaction of different microstructures with gradients in material properties, have limited the ability of currently existing methods to construct the assessment on the basis of actual failure mechanisms of bimetallic welds. Current work addresses the assessment procedure by combining experimental and numerical fracture mechanics comprising a micro-mechanical evaluation of the relevant damage mechanisms. The studied dissimilar ferrite (SA508)–austenite (AISI 304) circumferencial weld is one with a Ni-enriched buttering layer.The experimental work comprises tensile and fracture mechanical characterization of the different microstructural zones of the bimetallic weld. Tensile properties are determined with microstructure specific flat bar specimens as well as round bar specimens enabling better inference of true stress–strain curves. Fracture resistance curves are established by applying small-specimen testing techniques. Different crack configurations are modeled by finite element analysis (FEA) to assess the relationships between fracture types, toughness and local near crack tip constraint parameters. Transferability and characterization question are considered by determining J–Q-trajectories and employing small-scale yielding corrections (SSYCs). On the basis of the experimental and numerical results and a fractographical investigation, the micromechanics of fracture are interpreted. Differences in strain hardening capacities of microstructural zones are found to most severely affect the toughness transitions of the weld and the associated failure modes. Two prime failure types are noted, one for cracks located at outer heat affected zone (HAZ) resulting in an unstable crack deflection towards the fusion line (FL) and another type associated with cracks positioned near the fusion line, wherein a low-toughness ductile fracture process results. Small fracture mechanics specimen is found applicable for fracture resistance determination of bimetallic weldments.     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

Influence of hydrogen content on fracture toughness of CWSR Zr–2.5Nb pressure tube alloy

In this work, influence of hydrogen and temperature on the fracture toughness parameters of unirradiated, cold worked and stress relieved (CWSR) Zr–2.5Nb pressure tube alloys used in Indian Pressurized Heavy Water Reactor is reported. The fracture toughness tests were carried out using 17 mm width curved compact tension specimens machined from gaseously hydrogen charged tube-sections. Metallography of the samples revealed that hydrides were predominantly oriented along axial–circumferential plane of the tube. Fracture toughness tests were carried out in the temperature range of 30–300 °C as per ASTM standard E-1820-06, with the crack length measured using direct current potential drop (DCPD) technique. The fracture toughness parameters (J_Q, J_Max and dJ/da), were determined. The critical crack length (CCL) for catastrophic failure was determined using a numerical method. It was observed that for a given test temperature, the fracture toughness parameters representing crack initiation (J_Q) and crack propagation (J_Max, and dJ/da) is practically unaffected by hydrogen content. Also, for given hydrogen content, all the aforementioned fracture toughness parameters increased with temperature to a saturation value.     

Observations on the effect of post-weld heat treatment on J-resistance curves of sa-106b seamless piping welds

Ontario Hydro has developed a leak-before-break (LBB) methodology for application to large diameter piping (21, 22 and 24 inch) Schedule 100 SA106B heat transport (HT) piping as a design alternative to pipe whip restraints and in recognition of the questionable benefits of providing such devices. Ontario Hydro's LBB approach uses elastic-plastic fracture mechanics (EPFM).In order to assess the stability of HT piping in the presence of hypothetical flaws, the value of the material J-integral associated with crack extension (J— R curve) must be known. In a material test program J-resistance curves were determined from various pipe heats and four different welding procedures that were developed by Ontario Hydro for nuclear Class 1 piping. The test program was designed to investigate and quantify the effect of various factors such as test temperature, crack plane orientation and welding effects which have an influence on fracture properties. An acceptable lower bound J-resistance curve for the piping steels and welds were obtained by machining maximum thickness specimens from the pipes and weldments and by testing side-grooved compact tension specimens. This paper addresses the effect of test temperature and post-weld heat treatment on the J-resistance curves from the welds.The fracture toughness of all the welds at 250°C was lower than that at 20°C. Welds that were post-weld heat treated showed high crack initiation toughness, J_lc, rising J-resistance curves and stable and ductible crack extension. Non post-weld heat treated welds, while remaining tough and ductile, showed comparatively lower J_Ic, and J-resistance curves at 250°C. This drop in toughness is possibly due to a dynamic strain aging mechanism evidenced by serrated load-displacement curves. The fracture toughness of non post-weld heat treated welds increased significantly after a comparable post-weld heat treatment.The test procedure was validated by comparing three test results against independent tests conducted by Materials Engineering Associates (MEA) of Lanham, Maryland. The J_Ic and J-resistance curves obtained by Ontario Hydro and MEA were comparable.     

Analysis of stable crack growth of a semi-elliptical surface crack by numerical simulation

In the present paper, the canoeing effect during stable crack growth of a semi-elliptical surface crack in a side-grooved panel under tension was investigated by means of a three-dimensional elastic-plastic finite element analysis. The numerical crack growth simulation was performed by using crack mouth opening displacement resistance curves obtained from experiment on panels by the multi-specimen procedure. The influence of the crack tip constraint and the stress triaxiality on the ductile crack resistance property was studied. It is shown that the tearing modulus T_JR increases proportionally with decreasing stress triaxiality implying constraint dependent J_R-curves.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint

An extensive investigation has been carried out on the sensitivity parameters determination describing the fracture behaviour of the body with a crack with respect to the character change of the true stress–strain curve with the dominant region of Lueders deformation. This paper presents the consideration on the change judgement of the J-integral and the constraint as the base parameters of two-parameter fracture mechanics. The Weibull stress model for cleavage fracture originally proposed by Beremin group requires calibration of two micromechanics parameters (m, σ_u). The Weibull stress σ_w seems to be a parameter for the prediction of cleavage failure of cracked bodies and the study is focused on the assessment of the effects of constraint loss on the cleavage fracture toughness (J_c). To quantify the effects of the constraint variation on the cleavage fracture toughness the form of the toughness scaling model based on the Weibull stress σ_w is investigated. Local material parameters have been calculated from Beremin approach and the calibration is performed on various approaches. Methods are based on the weakest link assumption and the incremental fracture probability, which depends not only on the maximum principal stress, but also on the equivalent plastic strain. The fracture resistance has been assessed using data from static tests of three point bend specimens.     

Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J_R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.     

Evaluation of SCC crack behavior in zirconium and zircaloy-2 using nonlinear fracture mechanics parameters

Applicability of nonlinear fracture mechanics parameters, i.e. J-integral, crack tip opening displacement (CTOD), and crack tip opening angle (CTOA), to evaluation of stress corrosion crack (SCC) propagation rate was investigated using fully annealed zirconium plates and Zircaloy-2 tubing, both of which produce SCC with comparatively large plastic strain in an iodine environment at high temperatures.Tensile SCC tests were carried out at 300°C for center-notched zirconium plates and internal gas pressurization SCC tests at 350°C, for Zircaloy-2 tubing, to measure the SCC crack propagation rate. The J-integral around semi-elliptical SCC cracks produced in Zircaloy-2 tubing was calculated by a three-dimensional finite element method (FEM) code.The test results revealed that the SCC crack propagation rate dc/dt could be expressed as a function of the J-integral, which is the most frequently used parameter in nonlinear fracture mechanics, by the equation dc/dt = C · Jⁿ, where C and n were experimental constants.Among the other parameters, CTOD and CTOA, the latter appeared to be useful for assessing the crack propagation rate, because it had a tendency to hold a constant value at various crack depths.     

Use of the Master Curve methodology for real three dimensional cracks

At VTT, development work has been in progress for 15 years to develop and validate testing and analysis methods applicable for fracture resistance determination from small material samples. The VTT approach is a holistic approach by which to determine static, dynamic and crack arrest fracture toughness properties either directly or by correlations from small material samples. The development work has evolved a testing standard for fracture toughness testing in the transition region. The standard, known as the Master Curve standard is in a way “first of a kind”, since it includes guidelines on how to properly treat the test data for use in structural integrity assessment. No standard, so far, has done this. The standard is based on the VTT approach, but presently, the VTT approach goes beyond the standard. Key components in the standard are statistical expressions for describing the data scatter, and for predicting a specimens size (crack front length) effect and an expression (Master Curve) for the fracture toughness temperature dependence. The standard and the approach, it is based upon, can be considered to represent the state of the art of small specimen fracture toughness characterization. Normally, the Master Curve parameters are determined using test specimens with “straight” crack fronts and comparatively uniform stress state along the crack front. This enables the use of a single K_I value and single constraint value to describe the whole specimen. For a real crack in a structure, this is usually not the case. Normally, both K_I and constraint vary along the crack front and in the case of a thermal shock, even the temperature will vary along the crack front. A proper means of applying the Master Curve methodology for such cases is presented here.     

Tests on large scale LMFR piping Part I: crack resistance properties of through-cracked straight 700 mm nominal diameter pipes tested under bending at ambient temperature and 550°C

Knowing the crack resistance properties of a structure is essential for fracture mechanics safety analyses. Considerable attention has to be given in many cases to the through-wall case, since this is generally believed to be the controlling case with regard to complete pipe failure. Within a cooperative fracture mechanics programme of Electricite de France (EdF), Novatome and Siemens/KWU, bending tests with monotonously increasing load on circumferentially cracked straight pipes of typical liquid metal fast reactor (LMFR) main piping dimensions were performed. In this paper a summary report is given on crack resistance curves based on the crack tip parameters S, J and JM. The data are compared with those of C(T) specimens. The experiments have demonstrated an enormous potential for stable crack extension under global bending which is a typical loading for LMFR piping structures. The results of checking the transferability of laboratory specimen crack growth characteristics to the cracked pipes on the austenitic stainless steel 316 L demonstrate that the fracture mechanics concept for a reliable transfer of crack resistance data from small specimen geometries to large structures needs further qualification for high toughness materials.     

Use of J–R curves in assessing the fracture behavior of low upper shelf toughness materials

The objective of this investigation was to evaluate the use of small specimen J–R curves in assessing the fracture resistance behavior of reactor vessels containing low upper shelf (LUS) toughness weldments. As required by the U.S. Code of Federal Regulations (10 CFR, Part 50), reactor vessel beltline materials must maintain an upper shelf Charpy V-Notch (CVN) energy of at least 50 ft-lbs (68 J) throughout vessel life. If CVN values from surveillance specimens fall below this value, the utility must demonstrate to the U.S. Nuclear Regulatory Commission (NRC) that the lower values will provide “margins of safety against fracture equivalent to those required by Appendix G of the ASME Boiler and Pressure Vessel Code”. This paper will present recommendations regarding the material fracture resistance aspects of this problem and outline an analysis procedure for demonstrating adequate fracture safety based on CVN values.It is recommended that the deformation formulation of the J-integral be used in the analysis described above. For cases where J-integral fracture toughness testing will be required, the ASTM E1152-87 procedure should be followed, however, data should be taken to 50% to 60% of the specimen remaining ligament. Extension of the crack growth validity limits for J–R curve testing, as described in E1152-87, can be justified on the basis of a “J-controlled crack growth zone” analysis which shows an engineering basis for J-control to 25% to 40% of the specimen remaining ligament. If J-R curve extrapolations are required for the analysis, a simple power law fit to data in the extended validity region should be used. The example analysis performed for low upper shelf weld material, showed required CVN values for a reactor vessel with a 7.8 inch (198 mm) thick wall ranging from 32 ft-lbs (43 J) to 48 ft-lbs (65 J), depending on the magnitude of the thermal stress component.     

Ductile fracture parameters of RPV-materials

Ductile fracture material parameters have been determined for a reactor pressure vessel material to characterize its fracture resistance in the upper shelf toughness regime. Three different methods (the multiple specimen unloading (MSU), direct current potential drop (DCPD) and single specimen partial unloading compliance (SSPUC) methods) have been applied to test different CT-specimen geometries at temperatures between 25 and 300°C.It is shown that there are principle differences between J-R-curves measured by different experimental procedures, because of different methods for the measurement of crack lengths and crack growth. For instability analyses, using a complete J-R-curve, these differences seem to be negligible. For the determination of critical material parameters at or close to initiation of stable crack growth these differences may cause systematic errors tending to higher values for DCPD as compared to MSU-results and to lower values for SSPUC respectively.Procedures can be defined to evaluate comparable critical material parameters from the different experimental procedures, if J_i is known in a good approximation allowing to consider only the real crack extension without blunting, or if in addition the real (or realistically modelled) blunting and the effective blunting of the specific method are known. The differences in material parameters will depend quantitatively on the type of material and its toughness (slope of J-R-curve). They may be in the range of the experimental scatter observed in testing and seem to be negligible, but their systematic character should be kept in mind, e.g. when ranking different materials according to their critical parameters determined by different methods.     

Investigation of the ductile fracture properties of type 304 stainless steel plate, welds, and 4-inch pipe

J-integral fracture toughness tests were performed on welded 304 stainless steel 2-inch plate and 4-inch diameter pipe. The 2-inch plate was welded using a hot-wire automatic gas tungsten arc process. This weldment was machined into 1T and 2T compact specimens for single specimen unloading compliance J-integral tests. The specimens were cut to measure the fracure toughness of the base metal, weld metal and the heat affected zone (HAZ). The tests were performed at 550°F, 300°F and room temperature. The results of the J-integral tests indicate that the J_Ic of the base plate ranged from 4400 to 6100 in lbs/in² at 550°F. The J_Ic values for the tests performed at 300°F and room temperature were beyond the measurement capacity of the specimens and appear to indicate that J_Ic was greater than 8000 in lb/in². The J-integral tests performed on the weld metal specimens indicate that the J_Ic values ranged from 930 to 2150 in lbs/in² at 550°F. The J_Ic values of the weld metal specimens tested at 300°F and room temperature were 2300 and 3000 in lbs/in² respectively. One HAZ specimen was tested at 550°F and found to have a J_Ic value of 2980 in lbs/in² which indicates that the HAZ is an average of the base metal and weld metal thoughness. These test results indicate that there is a significant reduction in the initiation fracture toughness as a result of welding.The second phase of this task dealt with the fracture toughness testing of 4-inch diameter 304 stainless steel pipes containing a gas tungsten arc weld. The pipes were tested at 550°F in four point bending. Three tests were performed, two with a through wall flaw growing circumferentially and the third pipe had a part through radial flaw in combination with the circumferential flaw. These tests were performed using unloading compliance and d.c. potential drop crack length estimate methods. The results of these test indicate that the presence of a complex crack (radial and circumferential) reduces in the initiation toughness and the tearing modulus of the pipe material compared to a pipe with only a circumferentially growing crack.     

The importance of the triaxiality modified J concept for the assessment of pressurized components with surface flaws

With the progress of stable crack growth of surface flaws observed in panels or pressure vessels a canoe-shaped crack front is formed. The crack propagation in the longitudinal direction is more pronounced that in the wall thickness direction. Therefore, the canoe effect is important with respect to a leak-before-break assessment because the actual through crack length is influenced by this effect. Based on the J integral concept crack initiation and crack propagation in ductile materials are described by J resistance curves which were found to be dependent on the constraint effect of the specimen geometry. Prediction of local crack growth by taking a conservative (flat) J_R-curve into account results in a nonconservative estimate of the axial extension of the surface crack [W. Brocks, H. Veith and K. Wobst, in K. Kussmaul (ed.), Fracture Mechanics Verification by Large Scale Testing, Mech. Eng. Publication Limited, London, 1991]. This means that the influence of local constraint effects on crack resistance has to be considered.Ductile crack growth of semi-elliptical surface cracks in side-grooved specimens F(SCTsg) under tension made from German standard steel StE 460 will be reported on. The development of the canoe effect of an SCTsg specimen was also analysed by a finite element simulation of ductile crack growth which was modelled by using the node shift and node release technique and controlled by crack mouth opening displacement versus crack growth curves from the experiment. The simulation allows the determination of local J_R-curves in dependence on the local multiaxility of the stress state to verify the constraint modified J concept. It is demonstrate that the slope of the J_R-curves decreases with increasing multiaxiality of the stress state near by the crack front.     

Allowable minimum upper shelf toughness for nuclear reactor pressure vessels

The paper develops methodology and procedure for determining the allowable minimum upper shelf toughness for continued safe operation of nuclear reactor pressure vessels. Elastic-plastic fracture mechanics analysis method based on the J-integral tearing modulus (J/T) approach is used. Closed from expressions for the applied J and tearing modulus are presented for finite length, part-throughwall axial flaw with aspect ratio of . Solutions are then presented for Section III, Appendix G flaw. A simple flaw evaluation procedure that can be applied quickly by utility engineers is presented. An attractive feature of the simple procedure is that tearing modulus calculations are not required by the user, and a solution for the slope of the applied J/T line is provided. Results for the allowable minimum upper shelf toughness are presented for a range of reactor pressure vessel thickness and heatup/cooldown rates.     

Fracture toughness characterization of irradiated, low upper shelf welds

A data base of J − R curve trends is being established for irradiated, light-water reactor pressure vessel steels of low upper shelf toughness. R-curve trends have been developed for several welds made with Linde 80 flux and containing a high copper impurity which enhances the sensitivity to irradiation embrittlement. Tests were conducted using compact toughness specimens of 12.5 mm to 100 mm thickness. These data provide the materials properties necessary for a tearing instability analysis of postulated accident conditions in certain commercial power reactors. Irradiation decreased the level of the R curve significantly in most cases. Furthermore, the average value of tearing modulus (T_avg) was a more discriminating indicator of toughness degradation than the crack initiation toughness (J_Ic). Temperature-dependent correlations between the R-curve parameters (J_Ic, T_avg) and Charpy-V (C_v) upper shelf energy have been suggested here and in other programs. This finding could enhance the significance of C_v reactor surveillance data with respect to structural integrity. However, J_Ic and T_avg have demonstrated an inverse relationship with temperature which is not reflected in C_v upper shelf energy and this must be taken into account in the development of correlations.